Harbor freight is a cool place to ooh and aah in and they have cheap prices, but there's a reason why my family calls it "the junk tool store".
There is some good stuff in there, but definitely not a welder or a drill press.

Look at warranties when shopping. Harbor Freight has some decent warranties on some things.

"Buyer Beware" is a good thing to remember.

It's been my experience that the two places you don't want to get cheap is with guns and tools. You can get a deal and some good stuff can be had not not break the bank. But I've yet to have a cheap tool of any kind that held up long. In the long run you're better off to look for the best quality you can afford and keep an eye out for a deal.

The craigslist and pawn shop idea is a good one to keep an eye on.

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The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants. Thomas Jefferson

Cheap welders never work out. But there are inexpensive drill presses in your price range. The problem will be the capabilities of the drill press. A bench top model will do a lot of work, but may not have the capacity you need for something. You'll also want a decent drill press vise, which adds cost.

I've bought some tools at pawn shops, but it takes some searching to find the right ones. Harbor Freight will usually work, but wear out quickly or have a problem you can't get parts for. You don't need a machine-shop drill press for hobby work, but you do need accuracy.

Welders depend a lot on what you'll do and how experienced you are. For the price of a decent welder, you can have a gunsmith handle quite a few jobs for you.

Pull the handle to move the chuck to its lowest position then try to wiggle the chuck back and forth. The more play there is the worse the drill press is. A good one will have no or very very little play.